The OP mentioned "The cam is still locked in the closed position", so I have to assume that it is actually being locked. Partly tighten down the skewer with the cam open, then flip the cam to lock in place.
I like and trust the "vintage" internal cam skewers. They work very well. Steel or Stainless skewers?
Some nuts are knurled, some are not. I'm not sure it really makes that much difference. The knurled nuts will leave marks on your frame, but won't loosen (without stripped teeth as @
Davet suggested).
I've ridden bikes with horizontal dropouts for eons. Stand up and pedal, and the wheel will slip if it isn't tight. So, I've gotten a lot of practice getting my skewers almost as tight as I can get them without tools (cheaters).